John N. Treuer

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20202026

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math.CV2026

A new strong rigidity phenomenon for the Bergman metric

Peter Ebenfelt, John N. Treuer, Ming Xiao

We establish a new local-to-global rigidity phenomenon for the Bergman metric. Namely, under natural geometric hypotheses, a local conformal identification of Bergman metrics deter…

math.CV2025

The Levi $q$ -core and Property ( $P_{q}$ )

Gian Maria Dall'Ara, Samuele Mongodi, John N. Treuer

We introduce the Grassmannian $q$ -core of a distribution of subspaces of the tangent bundle of a smooth manifold. This is a generalization of the concept of the core previously int…

math.CV2025

Domains with Bergman metrics of constant curvature and Bergman-negligible subsets

Peter Ebenfelt, John N. Treuer, Ming Xiao

Let $D$ be a bounded domain in $C^{n}$ . Suppose the holomorphic sectional curvature of its Bergman metric equals a negative constant $τ$ . We show that $D$ is biholomorphic t…

math.CV2024

Rotational symmetries of domains and orthogonality relations

Soumya Ganguly, John N. Treuer

Let $Ω \subset C^{n}$ be a domain whose Bergman space contains all holomorphic monomials. We derive sufficient conditions for $Ω$ to be Reinhardt, complete Reinhardt, circula…

math.CV2023

Modifications of the Levi core

Tanuj Gupta, Emil J. Straube, John N. Treuer

We construct a family of subdistributions of the Levi core $C (N)$ called modified Levi cores ${M C_{A}}_{A}$ indexed…

math.CV2020

Rigidity theorem by the minimal point of the Bergman kernel

Robert Xin Dong, John Treuer

We use the Suita conjecture (now a theorem) to prove that for any domain $Ω \subset C$ its Bergman kernel $K (\cdot, \cdot)$ satisfies $K (z_{0}, z_{0}) = Volume (Ω)^{- 1}$ …